/*
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
*/

P.<x> = PolynomialRing(QQ)
g = P([1, 7, 12, -1, -8, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16, 2, -3*w^5 + 4*w^4 + 23*w^3 - 6*w^2 - 35*w - 6])

primes_array = [
[4, 2, -2*w^5 + 2*w^4 + 17*w^3 - w^2 - 27*w - 8],\
[11, 11, -w^5 + 2*w^4 + 6*w^3 - 5*w^2 - 7*w + 1],\
[11, 11, -w^5 + w^4 + 8*w^3 + w^2 - 12*w - 5],\
[11, 11, w - 1],\
[31, 31, -4*w^5 + 6*w^4 + 28*w^3 - 8*w^2 - 39*w - 11],\
[41, 41, -4*w^5 + 5*w^4 + 31*w^3 - 4*w^2 - 49*w - 16],\
[41, 41, w^4 - 3*w^3 - 3*w^2 + 8*w + 1],\
[41, 41, -w^2 + w + 2],\
[59, 59, w^2 - w - 4],\
[59, 59, 4*w^5 - 5*w^4 - 31*w^3 + 4*w^2 + 49*w + 14],\
[59, 59, -w^4 + 3*w^3 + 3*w^2 - 8*w - 3],\
[71, 71, 5*w^5 - 7*w^4 - 37*w^3 + 9*w^2 + 55*w + 16],\
[71, 71, -w^5 + 11*w^3 + 4*w^2 - 19*w - 7],\
[71, 71, -w^4 + 2*w^3 + 5*w^2 - 4*w - 4],\
[79, 79, 3*w^5 - 6*w^4 - 17*w^3 + 11*w^2 + 21*w + 7],\
[79, 79, -5*w^5 + 8*w^4 + 35*w^3 - 14*w^2 - 52*w - 11],\
[79, 79, -w^5 + 3*w^4 + 3*w^3 - 7*w^2 - 2*w + 2],\
[101, 101, -2*w^5 + 3*w^4 + 14*w^3 - 3*w^2 - 21*w - 9],\
[101, 101, -2*w^5 + 2*w^4 + 17*w^3 - 29*w - 9],\
[101, 101, -w^5 + 2*w^4 + 6*w^3 - 5*w^2 - 9*w + 1],\
[101, 101, -2*w^5 + 3*w^4 + 15*w^3 - 6*w^2 - 23*w - 4],\
[101, 101, -3*w^5 + 3*w^4 + 26*w^3 - 2*w^2 - 43*w - 13],\
[101, 101, -12*w^5 + 17*w^4 + 89*w^3 - 25*w^2 - 133*w - 30],\
[125, 5, -2*w^5 + 3*w^4 + 14*w^3 - 4*w^2 - 20*w - 8],\
[131, 131, -5*w^5 + 7*w^4 + 37*w^3 - 9*w^2 - 56*w - 17],\
[131, 131, w^4 - 3*w^3 - 3*w^2 + 7*w],\
[131, 131, w^5 - w^4 - 8*w^3 + 11*w + 5],\
[149, 149, w^5 - w^4 - 9*w^3 + 2*w^2 + 16*w + 3],\
[149, 149, -13*w^5 + 19*w^4 + 95*w^3 - 30*w^2 - 141*w - 28],\
[149, 149, 2*w^5 - 2*w^4 - 17*w^3 + 30*w + 8],\
[151, 151, -4*w^5 + 5*w^4 + 31*w^3 - 4*w^2 - 48*w - 14],\
[151, 151, -w^5 + 11*w^3 + 4*w^2 - 20*w - 9],\
[151, 151, 3*w^5 - 3*w^4 - 25*w^3 + 39*w + 12],\
[151, 151, 3*w^5 - 4*w^4 - 23*w^3 + 5*w^2 + 35*w + 11],\
[151, 151, 4*w^5 - 6*w^4 - 28*w^3 + 8*w^2 + 39*w + 10],\
[151, 151, -2*w^5 + 4*w^4 + 12*w^3 - 9*w^2 - 16*w - 1],\
[179, 179, w^5 - w^4 - 9*w^3 + w^2 + 18*w + 5],\
[179, 179, 4*w^5 - 5*w^4 - 31*w^3 + 6*w^2 + 46*w + 11],\
[179, 179, -7*w^5 + 10*w^4 + 51*w^3 - 12*w^2 - 78*w - 24],\
[191, 191, -3*w^5 + 5*w^4 + 20*w^3 - 8*w^2 - 29*w - 11],\
[191, 191, -w^5 + 3*w^4 + 4*w^3 - 10*w^2 - 4*w + 2],\
[191, 191, 12*w^5 - 16*w^4 - 91*w^3 + 19*w^2 + 138*w + 36],\
[211, 211, 5*w^5 - 7*w^4 - 37*w^3 + 10*w^2 + 55*w + 10],\
[211, 211, -7*w^5 + 9*w^4 + 54*w^3 - 10*w^2 - 83*w - 24],\
[211, 211, -w^5 + 11*w^3 + 4*w^2 - 21*w - 9],\
[229, 229, 7*w^5 - 10*w^4 - 51*w^3 + 14*w^2 + 75*w + 19],\
[229, 229, 6*w^5 - 7*w^4 - 48*w^3 + 5*w^2 + 75*w + 22],\
[229, 229, 6*w^5 - 9*w^4 - 42*w^3 + 11*w^2 + 62*w + 20],\
[239, 239, -12*w^5 + 16*w^4 + 91*w^3 - 19*w^2 - 139*w - 35],\
[239, 239, -8*w^5 + 12*w^4 + 58*w^3 - 20*w^2 - 87*w - 16],\
[239, 239, 5*w^5 - 7*w^4 - 37*w^3 + 10*w^2 + 55*w + 14],\
[269, 269, -5*w^5 + 7*w^4 + 37*w^3 - 10*w^2 - 53*w - 12],\
[269, 269, -7*w^5 + 9*w^4 + 54*w^3 - 10*w^2 - 82*w - 24],\
[269, 269, 5*w^5 - 7*w^4 - 37*w^3 + 10*w^2 + 54*w + 15],\
[331, 331, 7*w^5 - 10*w^4 - 51*w^3 + 12*w^2 + 77*w + 25],\
[331, 331, 8*w^5 - 11*w^4 - 59*w^3 + 13*w^2 + 87*w + 24],\
[331, 331, 3*w^5 - 3*w^4 - 25*w^3 + w^2 + 39*w + 12],\
[359, 359, -w^5 + 2*w^4 + 7*w^3 - 7*w^2 - 11*w + 3],\
[359, 359, -2*w^5 + 4*w^4 + 12*w^3 - 9*w^2 - 18*w - 3],\
[359, 359, 5*w^5 - 7*w^4 - 37*w^3 + 10*w^2 + 53*w + 14],\
[389, 389, -4*w^5 + 6*w^4 + 28*w^3 - 8*w^2 - 38*w - 13],\
[389, 389, 6*w^5 - 7*w^4 - 48*w^3 + 6*w^2 + 74*w + 21],\
[389, 389, -4*w^5 + 5*w^4 + 32*w^3 - 6*w^2 - 52*w - 13],\
[421, 421, -4*w^5 + 6*w^4 + 29*w^3 - 11*w^2 - 42*w - 8],\
[421, 421, -15*w^5 + 20*w^4 + 114*w^3 - 25*w^2 - 174*w - 43],\
[421, 421, 8*w^5 - 11*w^4 - 60*w^3 + 14*w^2 + 92*w + 22],\
[431, 431, 8*w^5 - 11*w^4 - 59*w^3 + 13*w^2 + 87*w + 23],\
[431, 431, 3*w^5 - 5*w^4 - 19*w^3 + 7*w^2 + 24*w + 6],\
[431, 431, 7*w^5 - 11*w^4 - 48*w^3 + 16*w^2 + 69*w + 18],\
[439, 439, -6*w^5 + 7*w^4 + 48*w^3 - 6*w^2 - 74*w - 19],\
[439, 439, 4*w^5 - 7*w^4 - 25*w^3 + 11*w^2 + 33*w + 8],\
[439, 439, 5*w^5 - 6*w^4 - 39*w^3 + 5*w^2 + 58*w + 16],\
[449, 449, -w^5 + 2*w^4 + 6*w^3 - 6*w^2 - 6*w + 1],\
[449, 449, w^5 - 2*w^4 - 5*w^3 + 2*w^2 + 4*w + 6],\
[449, 449, 4*w^5 - 5*w^4 - 31*w^3 + 4*w^2 + 50*w + 17],\
[449, 449, 6*w^5 - 9*w^4 - 43*w^3 + 13*w^2 + 65*w + 17],\
[449, 449, -3*w^5 + 3*w^4 + 25*w^3 - w^2 - 38*w - 10],\
[449, 449, -3*w^5 + 3*w^4 + 26*w^3 - 2*w^2 - 43*w - 12],\
[461, 461, 2*w^5 - 2*w^4 - 16*w^3 - 2*w^2 + 25*w + 9],\
[461, 461, 2*w^5 - 2*w^4 - 17*w^3 + w^2 + 26*w + 5],\
[461, 461, w^4 - 2*w^3 - 5*w^2 + 3*w + 6],\
[461, 461, -4*w^5 + 6*w^4 + 29*w^3 - 10*w^2 - 43*w - 12],\
[461, 461, w^5 - 3*w^4 - 4*w^3 + 9*w^2 + 6*w - 1],\
[461, 461, 3*w^5 - 5*w^4 - 20*w^3 + 9*w^2 + 26*w + 3],\
[479, 479, 15*w^5 - 21*w^4 - 111*w^3 + 28*w^2 + 167*w + 42],\
[479, 479, -4*w^5 + 6*w^4 + 29*w^3 - 11*w^2 - 43*w - 7],\
[479, 479, -9*w^5 + 12*w^4 + 68*w^3 - 14*w^2 - 104*w - 26],\
[491, 491, -8*w^5 + 11*w^4 + 59*w^3 - 13*w^2 - 87*w - 25],\
[491, 491, 7*w^5 - 11*w^4 - 48*w^3 + 16*w^2 + 69*w + 20],\
[491, 491, 3*w^5 - 5*w^4 - 19*w^3 + 7*w^2 + 24*w + 8],\
[499, 499, 3*w^5 - 4*w^4 - 23*w^3 + 5*w^2 + 35*w + 13],\
[499, 499, -7*w^5 + 10*w^4 + 51*w^3 - 12*w^2 - 77*w - 23],\
[499, 499, -2*w^5 + w^4 + 20*w^3 + 3*w^2 - 36*w - 12],\
[509, 509, -2*w^5 + 3*w^4 + 15*w^3 - 7*w^2 - 21*w - 1],\
[509, 509, -5*w^5 + 6*w^4 + 40*w^3 - 5*w^2 - 64*w - 19],\
[509, 509, 4*w^5 - 7*w^4 - 26*w^3 + 12*w^2 + 37*w + 11],\
[521, 521, 2*w^5 - w^4 - 19*w^3 - 4*w^2 + 30*w + 9],\
[521, 521, 5*w^5 - 8*w^4 - 35*w^3 + 14*w^2 + 52*w + 10],\
[521, 521, 5*w^5 - 6*w^4 - 40*w^3 + 6*w^2 + 62*w + 19],\
[529, 23, -6*w^5 + 8*w^4 + 46*w^3 - 11*w^2 - 71*w - 18],\
[529, 23, -4*w^5 + 5*w^4 + 30*w^3 - 3*w^2 - 44*w - 14],\
[529, 23, -5*w^5 + 6*w^4 + 39*w^3 - 4*w^2 - 58*w - 17],\
[541, 541, 2*w^5 - w^4 - 19*w^3 - 5*w^2 + 31*w + 15],\
[541, 541, w^5 - 3*w^4 - 4*w^3 + 10*w^2 + 3*w - 2],\
[541, 541, 5*w^5 - 7*w^4 - 37*w^3 + 9*w^2 + 54*w + 14],\
[569, 569, -3*w^5 + 4*w^4 + 23*w^3 - 6*w^2 - 34*w - 10],\
[569, 569, -2*w^5 + 3*w^4 + 15*w^3 - 6*w^2 - 24*w - 1],\
[569, 569, 5*w^5 - 6*w^4 - 39*w^3 + 4*w^2 + 60*w + 16],\
[571, 571, 5*w^5 - 7*w^4 - 37*w^3 + 9*w^2 + 54*w + 16],\
[571, 571, 5*w^5 - 6*w^4 - 40*w^3 + 6*w^2 + 64*w + 17],\
[571, 571, 2*w^5 - w^4 - 19*w^3 - 5*w^2 + 31*w + 13],\
[599, 599, 5*w^5 - 6*w^4 - 41*w^3 + 8*w^2 + 66*w + 15],\
[599, 599, 5*w^5 - 10*w^4 - 29*w^3 + 21*w^2 + 37*w + 5],\
[599, 599, 12*w^5 - 16*w^4 - 90*w^3 + 17*w^2 + 134*w + 39],\
[601, 601, 5*w^5 - 5*w^4 - 42*w^3 + w^2 + 67*w + 19],\
[601, 601, 9*w^5 - 13*w^4 - 65*w^3 + 17*w^2 + 96*w + 26],\
[601, 601, 5*w^5 - 6*w^4 - 40*w^3 + 5*w^2 + 64*w + 21],\
[631, 631, -8*w^5 + 11*w^4 + 60*w^3 - 14*w^2 - 91*w - 25],\
[631, 631, -4*w^5 + 6*w^4 + 28*w^3 - 7*w^2 - 40*w - 12],\
[631, 631, w^5 - 11*w^3 - 5*w^2 + 21*w + 12],\
[659, 659, -4*w^5 + 5*w^4 + 31*w^3 - 4*w^2 - 47*w - 18],\
[659, 659, -6*w^5 + 7*w^4 + 48*w^3 - 5*w^2 - 76*w - 24],\
[659, 659, 6*w^5 - 9*w^4 - 43*w^3 + 14*w^2 + 62*w + 17],\
[659, 659, 5*w^5 - 7*w^4 - 37*w^3 + 10*w^2 + 53*w + 13],\
[659, 659, -2*w^5 + 4*w^4 + 11*w^3 - 8*w^2 - 11*w],\
[659, 659, 6*w^5 - 8*w^4 - 45*w^3 + 9*w^2 + 68*w + 17],\
[691, 691, -4*w^5 + 7*w^4 + 26*w^3 - 12*w^2 - 38*w - 10],\
[691, 691, 4*w^5 - 5*w^4 - 32*w^3 + 6*w^2 + 52*w + 14],\
[691, 691, 6*w^5 - 7*w^4 - 48*w^3 + 6*w^2 + 74*w + 20],\
[701, 701, w^3 - 3*w^2 - 2*w + 3],\
[701, 701, -2*w^5 + 3*w^4 + 14*w^3 - 5*w^2 - 17*w - 2],\
[701, 701, -4*w^5 + 6*w^4 + 29*w^3 - 10*w^2 - 45*w - 8],\
[709, 709, 4*w^5 - 4*w^4 - 34*w^3 + w^2 + 56*w + 19],\
[709, 709, 4*w^5 - 6*w^4 - 28*w^3 + 9*w^2 + 36*w + 8],\
[709, 709, -5*w^5 + 7*w^4 + 37*w^3 - 8*w^2 - 57*w - 16],\
[709, 709, 7*w^5 - 11*w^4 - 48*w^3 + 17*w^2 + 68*w + 15],\
[709, 709, w^5 - 11*w^3 - 3*w^2 + 19*w + 3],\
[709, 709, -7*w^5 + 11*w^4 + 50*w^3 - 20*w^2 - 75*w - 16],\
[729, 3, -3],\
[739, 739, 5*w^5 - 7*w^4 - 36*w^3 + 7*w^2 + 52*w + 14],\
[739, 739, w^5 - w^4 - 9*w^3 + 18*w + 5],\
[739, 739, -7*w^5 + 9*w^4 + 54*w^3 - 10*w^2 - 84*w - 24],\
[769, 769, 5*w^5 - 6*w^4 - 40*w^3 + 6*w^2 + 63*w + 20],\
[769, 769, 4*w^5 - 6*w^4 - 29*w^3 + 9*w^2 + 45*w + 9],\
[769, 769, w^5 - 11*w^3 - 3*w^2 + 18*w + 2],\
[811, 811, 4*w^5 - 5*w^4 - 32*w^3 + 6*w^2 + 51*w + 13],\
[811, 811, 5*w^5 - 9*w^4 - 32*w^3 + 17*w^2 + 45*w + 11],\
[811, 811, 7*w^5 - 8*w^4 - 56*w^3 + 5*w^2 + 86*w + 27],\
[859, 859, -11*w^5 + 16*w^4 + 81*w^3 - 26*w^2 - 121*w - 23],\
[859, 859, -12*w^5 + 17*w^4 + 88*w^3 - 23*w^2 - 131*w - 32],\
[859, 859, 7*w^5 - 11*w^4 - 49*w^3 + 19*w^2 + 72*w + 13],\
[911, 911, -2*w^5 + w^4 + 20*w^3 + 3*w^2 - 37*w - 12],\
[911, 911, 2*w^5 - 2*w^4 - 17*w^3 + 2*w^2 + 27*w + 4],\
[911, 911, 6*w^5 - 8*w^4 - 45*w^3 + 7*w^2 + 70*w + 23],\
[919, 919, w^4 - 2*w^3 - 7*w^2 + 8*w + 6],\
[919, 919, 16*w^5 - 22*w^4 - 120*w^3 + 29*w^2 + 182*w + 46],\
[919, 919, -5*w^5 + 9*w^4 + 32*w^3 - 18*w^2 - 43*w - 11]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^4 + 4*x^3 - 9*x^2 - 16*x + 16
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, e, e, -3*e - 4, -e - 2, -e - 2, -e - 2, -1/2*e^3 - 5/2*e^2 + e + 8, -1/2*e^3 - 5/2*e^2 + e + 8, -1/2*e^3 - 5/2*e^2 + e + 8, 1/2*e^3 + 3/2*e^2 - 7*e - 4, 1/2*e^3 + 3/2*e^2 - 7*e - 4, 1/2*e^3 + 3/2*e^2 - 7*e - 4, 1/2*e^3 + 3/2*e^2 - 4*e, 1/2*e^3 + 3/2*e^2 - 4*e, 1/2*e^3 + 3/2*e^2 - 4*e, 1/2*e^3 + 7/2*e^2 + 5*e - 14, 1/2*e^3 + 7/2*e^2 + 5*e - 14, 1/2*e^3 + 3/2*e^2 - 6*e - 10, 1/2*e^3 + 7/2*e^2 + 5*e - 14, 1/2*e^3 + 3/2*e^2 - 6*e - 10, 1/2*e^3 + 3/2*e^2 - 6*e - 10, -3/2*e^3 - 17/2*e^2 + 4*e + 22, -e^3 - 3*e^2 + 9*e, -e^3 - 3*e^2 + 9*e, -e^3 - 3*e^2 + 9*e, -e^2 - e + 10, -e^2 - e + 10, -e^2 - e + 10, 1/2*e^3 + 7/2*e^2 - e - 20, 1/2*e^3 + 7/2*e^2 - e - 20, -e^3 - 3*e^2 + 5*e - 4, -e^3 - 3*e^2 + 5*e - 4, 1/2*e^3 + 7/2*e^2 - e - 20, -e^3 - 3*e^2 + 5*e - 4, -e^3 - 5*e^2 + 6*e + 20, -e^3 - 5*e^2 + 6*e + 20, -e^3 - 5*e^2 + 6*e + 20, -e^3 - 5*e^2 + 8, -e^3 - 5*e^2 + 8, -e^3 - 5*e^2 + 8, 1/2*e^3 + 9/2*e^2 + 5*e - 32, 1/2*e^3 + 9/2*e^2 + 5*e - 32, 1/2*e^3 + 9/2*e^2 + 5*e - 32, e^3 + 3*e^2 - 9*e - 6, e^3 + 3*e^2 - 9*e - 6, e^3 + 3*e^2 - 9*e - 6, -e^3 - 7*e^2 - 3*e + 28, -e^3 - 7*e^2 - 3*e + 28, -e^3 - 7*e^2 - 3*e + 28, e^3 + 3*e^2 - 9*e - 6, e^3 + 3*e^2 - 9*e - 6, e^3 + 3*e^2 - 9*e - 6, -e^3 - 2*e^2 + 16*e - 4, -e^3 - 2*e^2 + 16*e - 4, -e^3 - 2*e^2 + 16*e - 4, 2*e^3 + 8*e^2 - 9*e - 20, 2*e^3 + 8*e^2 - 9*e - 20, 2*e^3 + 8*e^2 - 9*e - 20, -e^3 - 2*e^2 + 18*e + 14, -e^3 - 2*e^2 + 18*e + 14, -e^3 - 2*e^2 + 18*e + 14, 1/2*e^3 + 7/2*e^2 - 2*e - 26, 1/2*e^3 + 7/2*e^2 - 2*e - 26, 1/2*e^3 + 7/2*e^2 - 2*e - 26, -3/2*e^3 - 11/2*e^2 + 11*e + 12, -3/2*e^3 - 11/2*e^2 + 11*e + 12, -3/2*e^3 - 11/2*e^2 + 11*e + 12, 5/2*e^3 + 27/2*e^2 - 5*e - 36, 5/2*e^3 + 27/2*e^2 - 5*e - 36, 5/2*e^3 + 27/2*e^2 - 5*e - 36, e^2 + 6*e + 10, e^2 + 6*e + 10, e^2 + 6*e + 10, 3/2*e^3 + 11/2*e^2 - 12*e - 6, 3/2*e^3 + 11/2*e^2 - 12*e - 6, 3/2*e^3 + 11/2*e^2 - 12*e - 6, 5/2*e^3 + 25/2*e^2 - 10*e - 26, -e^3 - 4*e^2 + 5*e + 2, -e^3 - 4*e^2 + 5*e + 2, -e^3 - 4*e^2 + 5*e + 2, 5/2*e^3 + 25/2*e^2 - 10*e - 26, 5/2*e^3 + 25/2*e^2 - 10*e - 26, -3/2*e^3 - 9/2*e^2 + 20*e + 8, -3/2*e^3 - 9/2*e^2 + 20*e + 8, -3/2*e^3 - 9/2*e^2 + 20*e + 8, -3/2*e^3 - 17/2*e^2 + 5*e + 24, -3/2*e^3 - 17/2*e^2 + 5*e + 24, -3/2*e^3 - 17/2*e^2 + 5*e + 24, -2*e^3 - 9*e^2 + 8*e + 20, -2*e^3 - 9*e^2 + 8*e + 20, -2*e^3 - 9*e^2 + 8*e + 20, 3/2*e^3 + 13/2*e^2 - 4*e - 34, 3/2*e^3 + 13/2*e^2 - 4*e - 34, 3/2*e^3 + 13/2*e^2 - 4*e - 34, 1/2*e^3 + 7/2*e^2 - 2*e + 2, 1/2*e^3 + 7/2*e^2 - 2*e + 2, 1/2*e^3 + 7/2*e^2 - 2*e + 2, 5/2*e^3 + 23/2*e^2 - 5*e - 34, 5/2*e^3 + 23/2*e^2 - 5*e - 34, 5/2*e^3 + 23/2*e^2 - 5*e - 34, -1/2*e^3 - 1/2*e^2 + 7*e - 14, -1/2*e^3 - 1/2*e^2 + 7*e - 14, -1/2*e^3 - 1/2*e^2 + 7*e - 14, -1/2*e^3 - 9/2*e^2 - 6*e + 18, -1/2*e^3 - 9/2*e^2 - 6*e + 18, -1/2*e^3 - 9/2*e^2 - 6*e + 18, 3/2*e^3 + 11/2*e^2 - 16*e - 28, 3/2*e^3 + 11/2*e^2 - 16*e - 28, 3/2*e^3 + 11/2*e^2 - 16*e - 28, -e^3 - 3*e^2 + e - 12, -e^3 - 3*e^2 + e - 12, -e^3 - 3*e^2 + e - 12, 3*e^3 + 13*e^2 - 13*e - 26, 3*e^3 + 13*e^2 - 13*e - 26, 3*e^3 + 13*e^2 - 13*e - 26, 1/2*e^3 + 1/2*e^2 - 13*e + 4, 1/2*e^3 + 1/2*e^2 - 13*e + 4, 1/2*e^3 + 1/2*e^2 - 13*e + 4, -e^3 - 6*e^2 - 5*e + 40, -2*e^3 - 8*e^2 + 7*e + 8, -2*e^3 - 8*e^2 + 7*e + 8, -2*e^3 - 8*e^2 + 7*e + 8, -e^3 - 6*e^2 - 5*e + 40, -e^3 - 6*e^2 - 5*e + 40, 1/2*e^3 - 5/2*e^2 - 14*e + 28, 1/2*e^3 - 5/2*e^2 - 14*e + 28, 1/2*e^3 - 5/2*e^2 - 14*e + 28, -2*e^2 - 8*e - 2, -2*e^2 - 8*e - 2, -2*e^2 - 8*e - 2, -e^3 - 8*e^2 - 4*e + 38, -3/2*e^3 - 7/2*e^2 + 14*e + 6, -e^3 - 8*e^2 - 4*e + 38, -3/2*e^3 - 7/2*e^2 + 14*e + 6, -e^3 - 8*e^2 - 4*e + 38, -3/2*e^3 - 7/2*e^2 + 14*e + 6, -e^3 - 3*e^2 + 24*e + 26, -1/2*e^3 + 1/2*e^2 + 13*e - 8, -1/2*e^3 + 1/2*e^2 + 13*e - 8, -1/2*e^3 + 1/2*e^2 + 13*e - 8, 2*e^2 - 2*e - 14, 2*e^2 - 2*e - 14, 2*e^2 - 2*e - 14, -1/2*e^3 - 1/2*e^2 + 17*e + 16, -1/2*e^3 - 1/2*e^2 + 17*e + 16, -1/2*e^3 - 1/2*e^2 + 17*e + 16, 3*e^2 + 2*e - 36, 3*e^2 + 2*e - 36, 3*e^2 + 2*e - 36, 3/2*e^3 + 13/2*e^2 - 11*e - 52, 3/2*e^3 + 13/2*e^2 - 11*e - 52, 3/2*e^3 + 13/2*e^2 - 11*e - 52, 5/2*e^3 + 19/2*e^2 - 15*e - 12, 5/2*e^3 + 19/2*e^2 - 15*e - 12, 5/2*e^3 + 19/2*e^2 - 15*e - 12]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([4, 2, -2*w^5 + 2*w^4 + 17*w^3 - w^2 - 27*w - 8])] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]